Find the value of $ sec( heta) $ when $ heta $ is on the unit circle

Given that $ \theta $ is an angle on the unit circle, we know that:

$ \sec(\theta) = \frac{1}{\cos(\theta)} $

The cosine of $ \theta $ can be found using the coordinates (x, y) of the corresponding point on the unit circle, where x represents $ \cos(\theta) $.

Suppose $ \theta = \frac{\pi}{4} $, then:

$ \cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} $

Therefore:

$ \sec\left(\frac{\pi}{4}\right) = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2} $

To find $ sec( heta) $ for $ heta $ on the unit circle, recall:

$ sec( heta) = frac{1}{cos( heta)} $

If $ heta = frac{pi}{3} $, then:

$ cosleft(frac{pi}{3}
ight) = frac{1}{2} $

Thus:

$ secleft(frac{pi}{3}
ight) = 2 $

For $ heta $ on the unit circle:

$ sec( heta) = frac{1}{cos( heta)} $

When $ heta = frac{pi}{6} $,

$ cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2} $

So:

$ secleft(frac{pi}{6}
ight) = frac{2}{sqrt{3}} $

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